Theresa May has been given 28 days to take the case to the supreme court before the appeal judges' ruling takes effect. Photograph: Dan Kitwood/Getty Images

The home secretary, Theresa May, is facing urgent pressure to overhaul the criminal records system after an appeal court ruled that the way it operated was unlawful and breached human rights.

One of Britain's most senior judges, Lord Dyson, the master of rolls, ruled that a blanket requirement on job applicants to disclose minor offences, including cautions, amounted to a breach of their right to a private and family life.

In an unusual move, the publication of the judgment was delayed from December to give the Home Office time to prevent the implications of the ruling plunging the criminal record checks system into chaos.

But after a hearing on Friday, Dyson said: "It is extraordinary that nothing has been done. The government needs to pull its finger out and introduce legislation."

The formal judgment published on Tuesday involved a 21-year-old man identified in court as "T", who was given warnings by Greater Manchester police when he was 11 over two stolen bicycles.

He was asked to disclose the cautions – even though they were spent under the Rehabilitation of Offenders Act 1974 – when he applied for a job at a football club at the age of 17 and when he applied to a university sports studies course.

The appeal court also upheld a second case involving "JB", who was cautioned in 2001 when she was in her early 40s for stealing a packet of false nails from a chemist in Sheffield. Ten years later she was turned down for a job working with vulnerable adults, despite completing a six-week training course. The case shows that the ruling applies to minor offences committed by adults as well as juveniles.

Four million people a year who apply to work with children or vulnerable adults have to provide either a standard or enhanced criminal records certificate. Both types of check involve the disclosure of all convictions and cautions, including those deemed spent under the 1974 legislation.

The ruling by three appeal court judges invites the home secretary to take the case to the supreme court within 28 days, otherwise the ruling that the current system is unlawful will take effect.

The judges said they did not accept the Home Office's argument that it was not within their discretion to make a declaration that the current law was incompatible with human rights because parliament was considering the matter.

"This is not a case where we can be confident that parliament will move swiftly to find a solution. In these circumstances, we consider that it is appropriate to make a declaration. We accordingly allow T's appeal," they said.

The master of the rolls said he accepted that the disclosure of old convictions and cautions was sought with the aim of protecting children and vulnerable adults, but added: "The statutory regime requiring the disclosure of all convictions and cautions relating to recordable offences is disproportionate to that legitimate aim."

The appeal court objected to the scheme because disclosure had to be made regardless of its relevance to the position applied for.

The court also found that the disclosure system had the potential to interfere with privacy rights because "as a conviction recedes into the past, it becomes part of the individual's private life" and "the administering of a caution is part of an individual's private life from the outset".

It noted that "the disclosure of historic information about convictions … can lead to a person's exclusion from employment".

Corinna Ferguson, legal officer for Liberty, which was party to the case, said: "This sensible judgment requires the government to introduce a more nuanced system for disclosing this type of sensitive personal data to employers.

"For too long irrelevant and unreliable information provided under the blanket CRB system has blighted people's lives. We hope that long overdue reforms – properly balancing the aim of public protection with privacy rights – will now be forthcoming."

A government spokesman said: "The protection of children and vulnerable groups must not be compromised. We are disappointed by this judgment and are seeking leave to appeal to the supreme court."